Question

cos^2 45 + cos^2 30 + cosec^2 30

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Answer 1

cos²45 + cos²30 + cosec²30

Answer 2

Given Expression is

$\rm {cos}^{2} 45\degree + {cos}^{2} 30 \degree + {cosec}^{2} 30 \degree$

Find the value of the given Expression.

Solution :-

Let's solve this problem by using, trignometric values of angles

cos(45)° = 1/√2

cos(30)° = (√3)/2

cosec(30)° = 2

then, on substituting the values

$\rm⇢ \: \: {( \frac{1}{ \sqrt{2} }) }^{2} + {( \frac{ \sqrt{3} }{2} )}^{2} + {( 2) }^{2}$

$\rm⇢ \: \: \frac{1}{2} + \frac{3}{4} + 4$

$\rm⇢ \: \: \frac{2 + 3 + 16}{4}$

$\rm⇢ \: \: \frac{21}{4}$

✏ FINAL ANSWER :-

The Value of

$\textbf{\textsf{\red⇢ \orange{cos²(45)\degree + cos² (30)\degree + cosec²(30)\degree} = }} \green{\bf{ \frac{21}{4}} }$